Make sure fully comprehensive insurance is built in to the price. You will have to pay an insurance

Most online car rental companies offer an automatic online discount. Some also cater for a delivery and collection auto rentals service, from/ to the airport, major towns or resort. This would be the same scenario for the local car rental company also.
Make sure fully comprehensive insurance is built in to the price. You will have to pay an insurance excess on top of this. Minimum rental is usually two days but sometimes 3 days. Get them to throw in a free road map with the deal, most car rental places should be doing this anyway. Great for pinpointing those twisty back roads.
This really varies depending auto rentals on season, type of car and rental method. I prefer to use the local car hire company. I always find you're charged that little extra with the major car rental firms. Also, I find booking a car through one of those search boxes/ middle men, prone to error. It's not always the case, but I have turned up at the rentals desk in Larnaca airport to find out your Ford Fiesta you booked is actually an Opel Astra. Or, being charged extra for something, which was not stated on the original agreement. You don't need that hassle at the start of your holiday.